Equivalence of metric homomorphisms

Suppose $K$ is an algebra with involution over $k$ and $A$, $B$ are $K$-modules on which are defined $\varepsilon$-Hermitian $K$-invariant forms with values in $k$. Metric homomorphisms of the module $A$ into the module $B$ are called equivalent in the broad sense if one can be obtained from the other by multiplying by automorphisms of both modules, and equivalent in the narrow sense if one can be obtained from the other by multiplying by an automorphism of $B$. Necessary and sufficient conditions are given for the broad and narrow equivalence of two metric homomorphisms of one semisimple module of finite length into another. As a consequence, a classification of representations of one quadratic form by means of another is obtained.